Problem: Solve for $x$ and $y$ using elimination. ${2x-2y = 14}$ ${-2x+5y = -5}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {2x-2y = 14}\thinspace$ to find $x$ ${2x - 2}{(3)}{= 14}$ $2x-6 = 14$ $2x-6{+6} = 14{+6}$ $2x = 20$ $\dfrac{2x}{{2}} = \dfrac{20}{{2}}$ ${x = 10}$ You can also plug ${y = 3}$ into $\thinspace {-2x+5y = -5}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(3)}{= -5}$ ${x = 10}$